The $\ell_\infty$ Perturbation of HOSVD and Low Rank Tensor Denoising

Abstract

The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recent progress has been made in Richard and Montanari [2014], Zhang and Xia [2017] and Liu et al. [2017] demonstrating that minimax optimal singular spaces… (More)